Speaking at a late night press conference in Strasbourg following talks with EU Commission president Jean-Claude Juncker, May said: "The deal that MPs voted on in January was not strong enough in making that clear – and legally binding changes were needed to set that right.

"Today we have agreed them."

The UK and the EU have now signed off on two documents designed to bolster the Brexit withdrawal agreement and accompanying political declaration on Britain's future.

The first is a "joint legally binding instrument" which May said had "comparable legal weight" to the Brexit agreement itself and would "guarantee that the EU cannot act with the intent of applying the backstop indefinitely".

"If they do, it can be challenged through arbitration and if they are found to be in breach the UK can suspend the backstop," the prime minister said.

"The joint instrument also gives a legal commitment that whatever replaces the backstop does not need to replicate it."

The two sides have also published a "joint statement" which commits to replacing the backstop with "alternative arrangements" by the end of December 2020.

"There will be a specific negotiating track on alternative arrangements from the very start of the next phase of negotiations," May promised.

"It will consider facilitations and technologies – both those currently ready and emerging."

May also promised a "Unilateral Declaration" from the UK government, saying that ministers believe "there would be nothing to prevent the UK instigating measures that would ultimately dis-apply the backstop" if talks with the EU break down.

“Political crisis”

Speaking in the House of Commons as May announced the agreement, Cabinet Office minister and her de-facto deputy David Lidington said MPs would face a "fundamental choice” later today "to vote for the improved deal or to plunge this country into a political crisis".

"If we vote for the improved deal we will both end the current uncertainty and deliver Brexit," he said.

"The House was clear on the need for legally binding changes to the backstop. Today, we have secured those changes.

"Now is the time to come together to back this improved Brexit deal and to deliver on the instruction of the British people."

A DUP spokesman said: "We note the prime minister’s latest statement and update on our EU exit negotiations. These publications need careful analysis. We will be taking appropriate advice, scrutinising the text line by line and forming our own judgement.

"We will measure this latest text against the Brady amendment and the commitments made by the prime minister on 29 January."